Rewrite as a simplified fraction. ${0.70\overline{7} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 707.7777...\\ 100x &= 70.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 637}$ ${x = \dfrac{637}{900}} $